Socrate
I know that I know nothing.
Misconceptions
Socrates said "I know that I know nothing".
The formula is not in Plato's Apology, our earliest witness of the trial. The text says something more precise: Socrates judges himself "a little wiser" than a man reputed learned because "what I do not know I do not think I know either". He even adds that he knows one thing: that it is wrong to do wrong and to disobey one who is wiser. The form closest to the famous formula is in Diogenes Laertius, six centuries after him: "he knew nothing except just the fact of his ignorance". It is not absurd, since it keeps an exception, but it is more radical than the Apology, where Socrates says he knows at least that doing wrong is evil. Socrates may have said something similar; the exact sentence does not come from a direct witness.
The Socrates of Plato's dialogues is the real Socrates.
We cannot say so. Plato is an extraordinary witness, but he is also a philosopher with his own doctrine (the Forms, the immortal soul). Diogenes Laertius already remarks that Plato himself treats subjects (Anaxagoras' physics) which Socrates, in the Apology, said he left aside, while putting everything into Socrates' mouth. Aristotle points out that they must not be confused: Socrates sought universal definitions but did not separate them from the sensible world; it is the Platonists who made them separate Forms.
Socrates was interested only in morality and never in nature.
This is the picture given by Aristotle and Xenophon: he would have left nature aside to seek the universal in ethics. Diogenes Laertius disagrees: "in my opinion Socrates discoursed on physics as well as on ethics", since he often speaks of Providence, even according to Xenophon. On this point our witnesses contradict one another.